I Normally use following way to extract the URLs and it's realted Texts from $meach, and it works well as of now.

my @links = $mech->links;
foreach $href_links (@links)
{
    #URL
    my $lnk = $href_links->url();

    #Text
    my $txt = $href_links->text();
    print $lnk."\t".$txt."\n";
}
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Would you be able to post the contents of the html page to PerlMonks? (Capture the event just before you run the foreach loop)

print $mech->content
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, I am Not able to get clear pitcure as what output you want Vs What is there on the html page.